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Lineární algebraické modelování úloh s nepřesnými daty / Lineární algebraické modelování úloh s nepřesnými daty

In this thesis we consider problems Ax b arising from the discretization of ill-posed problems, where the right-hand side b is polluted by (unknown) noise. It was shown in [29] that under some natural assumptions, using the Golub-Kahan iterative bidiagonalization the noise level in the data can be estimated at a negligible cost. Such information can be further used in solving ill-posed problems. Here we suggest criteria for detecting the noise revealing iteration in the Golub-Kahan iterative bidiagonalization. We discuss the presence of noise of different colors. We study how the loss of orthogonality affects the noise revealing property of the bidiagonalization.

Identiferoai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:300525
Date January 2011
CreatorsVasilík, Kamil
ContributorsHnětynková, Iveta, Janovský, Vladimír
Source SetsCzech ETDs
LanguageEnglish
Detected LanguageEnglish
Typeinfo:eu-repo/semantics/masterThesis
Rightsinfo:eu-repo/semantics/restrictedAccess

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